If the distribution of the data across the rolling windows is stationary
then there are a few things that you can do. The sample mean, for example,
computed using the overlapping data follows a MA(h-1) process where h is the
number of overlapping data periods. You can use this to get correct standard
errors for the mean estimate. Alternatively, you can utilize non-prametric
corrections to estimate the true standard error of the mean with serially
correlated data. One popular such method used in econometrics is the
Newey-West estimator.
"Patrick Agin" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> Hi,
> I observe on a daily basis the realization of a random variable x on a
> given history of N points in the past and I am interested in the
> probability density function of the sum of x over a month (say 30 days).
> To increase the size of my sample, I roll a window of width 30 each day
> and collect (N-30+1) observations (instead of having N/30 independant
> observations only). Obviously, the collected sums are highly correlated
> and the PDF is distorted.
>
> Does it exist a statistical correction to make in order to adjust the
> distribution so it reflects better the reality?
>
> Thank you very much,
> Patrick
>
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